[gcc] GCC 4.5.0=>4.5.1

gcc/mpfr/cbrt.c

-/* mpfr_cbrt -- cube root function.
-
-Copyright 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
-Contributed by the Arenaire and Cacao projects, INRIA.
-
-This file is part of the GNU MPFR Library.
-
-The GNU MPFR Library is free software; you can redistribute it and/or modify
-it under the terms of the GNU Lesser General Public License as published by
-the Free Software Foundation; either version 2.1 of the License, or (at your
-option) any later version.
-
-The GNU MPFR Library is distributed in the hope that it will be useful, but
-WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
-License for more details.
-
-You should have received a copy of the GNU Lesser General Public License
-along with the GNU MPFR Library; see the file COPYING.LIB.  If not, write to
-the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
-MA 02110-1301, USA. */
-
-#define MPFR_NEED_LONGLONG_H
-#include "mpfr-impl.h"
-
- /* The computation of y = x^(1/3) is done as follows:
-
-    Let x = sign * m * 2^(3*e) where m is an integer
-
-    with 2^(3n-3) <= m < 2^(3n) where n = PREC(y)
-
-    and m = s^3 + r where 0 <= r and m < (s+1)^3
-
-    we want that s has n bits i.e. s >= 2^(n-1), or m >= 2^(3n-3)
-    i.e. m must have at least 3n-2 bits
-
-    then x^(1/3) = s * 2^e if r=0
-         x^(1/3) = (s+1) * 2^e if round up
-         x^(1/3) = (s-1) * 2^e if round down
-         x^(1/3) = s * 2^e if nearest and r < 3/2*s^2+3/4*s+1/8
-                   (s+1) * 2^e otherwise
- */
-
-int
-mpfr_cbrt (mpfr_ptr y, mpfr_srcptr x, mp_rnd_t rnd_mode)
-{
-  mpz_t m;
-  mp_exp_t e, r, sh;
-  mp_prec_t n, size_m, tmp;
-  int inexact, negative;
-  MPFR_SAVE_EXPO_DECL (expo);
-
-  /* special values */
-  if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
-    {
-      if (MPFR_IS_NAN (x))
-        {
-          MPFR_SET_NAN (y);
-          MPFR_RET_NAN;
-        }
-      else if (MPFR_IS_INF (x))
-        {
-          MPFR_SET_INF (y);
-          MPFR_SET_SAME_SIGN (y, x);
-          MPFR_RET (0);
-        }
-      /* case 0: cbrt(+/- 0) = +/- 0 */
-      else /* x is necessarily 0 */
-        {
-          MPFR_ASSERTD (MPFR_IS_ZERO (x));
-          MPFR_SET_ZERO (y);
-          MPFR_SET_SAME_SIGN (y, x);
-          MPFR_RET (0);
-        }
-    }
-
-  /* General case */
-  MPFR_SAVE_EXPO_MARK (expo);
-  mpz_init (m);
-
-  e = mpfr_get_z_exp (m, x);                /* x = m * 2^e */
-  if ((negative = MPFR_IS_NEG(x)))
-    mpz_neg (m, m);
-  r = e % 3;
-  if (r < 0)
-    r += 3;
-  /* x = (m*2^r) * 2^(e-r) = (m*2^r) * 2^(3*q) */
-
-  MPFR_MPZ_SIZEINBASE2 (size_m, m);
-  n = MPFR_PREC (y) + (rnd_mode == GMP_RNDN);
-
-  /* we want 3*n-2 <= size_m + 3*sh + r <= 3*n
-     i.e. 3*sh + size_m + r <= 3*n */
-  sh = (3 * (mp_exp_t) n - (mp_exp_t) size_m - r) / 3;
-  sh = 3 * sh + r;
-  if (sh >= 0)
-    {
-      mpz_mul_2exp (m, m, sh);
-      e = e - sh;
-    }
-  else if (r > 0)
-    {
-      mpz_mul_2exp (m, m, r);
-      e = e - r;
-    }
-
-  /* invariant: x = m*2^e, with e divisible by 3 */
-
-  /* we reuse the variable m to store the cube root, since it is not needed
-     any more: we just need to know if the root is exact */
-  inexact = mpz_root (m, m, 3) == 0;
-
-  MPFR_MPZ_SIZEINBASE2 (tmp, m);
-  sh = tmp - n;
-  if (sh > 0) /* we have to flush to 0 the last sh bits from m */
-    {
-      inexact = inexact || ((mp_exp_t) mpz_scan1 (m, 0) < sh);
-      mpz_div_2exp (m, m, sh);
-      e += 3 * sh;
-    }
-
-  if (inexact)
-    {
-      if (negative)
-        rnd_mode = MPFR_INVERT_RND (rnd_mode);
-      if (rnd_mode == GMP_RNDU
-          || (rnd_mode == GMP_RNDN && mpz_tstbit (m, 0)))
-        inexact = 1, mpz_add_ui (m, m, 1);
-      else
-        inexact = -1;
-    }
-
-  /* either inexact is not zero, and the conversion is exact, i.e. inexact
-     is not changed; or inexact=0, and inexact is set only when
-     rnd_mode=GMP_RNDN and bit (n+1) from m is 1 */
-  inexact += mpfr_set_z (y, m, GMP_RNDN);
-  MPFR_SET_EXP (y, MPFR_GET_EXP (y) + e / 3);
-
-  if (negative)
-    {
-      MPFR_CHANGE_SIGN (y);
-      inexact = -inexact;
-    }
-
-  mpz_clear (m);
-  MPFR_SAVE_EXPO_FREE (expo);
-  return mpfr_check_range (y, inexact, rnd_mode);
-}